The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2 X^2+X  X X^2  0
 0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0
 0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0

generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+15x^12+96x^14+15x^16+1x^28

The gray image is a linear code over GF(2) with n=56, k=7 and d=24.
This code was found by Heurico 1.16 in 0.000987 seconds.